I'm looking if there is a way to repeat the "led blinking" continuously in the background
That implies a foreground that is distinct from the background. That is not possible on the Arduino, since it has just one processor.
The loop() function is (or should be) called hundreds of thousands of times per second. Most of the time, it should accomplish nothing. Now and then, it should determine that it is time to change state, and should react accordingly. The blink without delay example shows how this works.
Think about how you would cook bacon and eggs for breakfast. Is it possible for you to be cooking both at once? Of course it is, even though there is only one of you. Periodically, you check to see if it is time to turn the bacon. Periodically, you check to see if it is time to turn the eggs. Periodically, you check to see if the bacon is done. Periodically, you check to see if the eggs are done.
Now, suppose that you want toast and coffee with your bacon and eggs. You can imagine, easily, I'm guessing, how you would handle checking on the toast and coffee while the eggs and bacon are cooking.